Metamath Proof Explorer

Theorem nfcri

Description: Consequence of the not-free predicate. (Contributed by Mario Carneiro, 11-Aug-2016) Avoid ax-10 , ax-11 . (Revised by Gino Giotto, 23-May-2024) Avoid ax-12 (adopting Wolf Lammen's 13-May-2023 proof). (Revised by SN, 3-Jun-2024)

Ref Expression
Hypothesis nfcri.1
|- F/_ x A
Assertion nfcri
|- F/ x y e. A


Step Hyp Ref Expression
1 nfcri.1
 |-  F/_ x A
2 nfcr
 |-  ( F/_ x A -> F/ x y e. A )
3 1 2 ax-mp
 |-  F/ x y e. A